D1 - Gravitational Fields Flashcards
what is gravity
all mass attracts all other mass
what is the gravitational force eq
F = GMm/r^2
what are the relationships present in the gravitational force eq
F is directly proportional to Mm and inversely proportional to r^2
what are the si units for the grav constant
kg-1m3s-2
what is newtons shell theorem
a spherically symmetric shell of mass M acts as if all of its mass is located at the centre
determine the force of gravitational attraction between the earth (m- 5.98 x 10^24kg) and a 70kg student if the student is in an airplane at 40000ft above the earths surface. this would place them 6.39 x 10^6m from the earths centre
F = GMm/r^2
F = (6.67x10^-11) x (5.98 x 10^24)(70)/(6.39 x 10^6)^2
F = 683.79N
what is a vector field
a field that describes the force that would act on a particle at various positions
what is the formula for an electric field
E = force/charge
how does mass relate to the distortion of space
the larger the mass, the more space that it distorted
how do we represent the strength of a field
vector length
vector density
what is a newton in si units
kgms-2
what does ‘r’ mean in the gravitational force eq in relation to the earth
r = radius of the whole orbit to the centre of earth
what is the formula for gravitational field strength
g=GM/r^2
what is the gravitational field strength halfway between the centres of the earth and the moon?
M of earth = 6 x 10^24kg
m of moon = 7.3 x 10^22kg
radius between earth and moon = 3.8 x 10^8m
g = GM/r^2
g = (6.67 x 10^-11)(6x10^24)/(1.9x10^8)^2
g = 0.011 of earth
g = (6.67x10^-11)(7.3 x 10^22)/(1.9x10^8)^2
g = 1.35x10^-4
0.011-1.35x10^-4 = 0.0109Nkg^-1 to the earth
what happens to the work done the further you go from a planet
GPE increases with distance, but if an object is far enough away from the planet, the grav force is negligible
what is teh formula for grav potential (V)
V = W/m
Grav potential = work done/ mass
what is the grav potential energy at infinity
zero
what is gravitational potential
the gravitational potential energy per unit of mass
when drawing equipotentials around the earth to represent grav potential, what do you notice about the spaces between the lines?
the equipotentials get more spaced out
Does the grav potential start from negative or positive? why
negative.
as the distance from the earth increases, the grav potential gets closer to zero, and so the closer distances have to have a negative grav potential for this to happen
as the distance from the earth increases, the grav potential…
decreases, because the point is further away from the grav. field
what does the potential gradient equal
gravitational field strength
what is the work done by a mass when it is moved along an equipotential surface
no work is done, when a mass is moved ALONG an equipotential line
calculate the minimum work required to lift an astronaut of mass 80kg from the earth’s surface to the height of the ISS (300km).
earth radius = 6400km
earth mass = 6x10^24
g = 6.67 x 10^-11
Work done = mass x change in grav potential
change in grav potential = grav potential at earth - grav potential at ISS
grav potential at earth = 6.26x10^7
grav potential at ISS = -5.97 x 10^7
6.26x10^7 - 5.97 x 10^7 = 2.9 x 10^6
(2.9 x10^6)(80) = 232000000J or 232MJ
what is the formula for potential gradient
change in grav potential/change in radius
